IQ modulation is a technique of encoding a carrier with information by controlling both the magnitude and phase of the carrier. An IQ modulator is supplied with a carrier, an in-phase control input I and a quadrature control input Q. The IQ modulator modifies the amplitude and phase of the carrier in accordance with the values of the control inputs. In its most general form the amplitude and phase of the modulated carrier can vary independently and in continuous fashion. In some modulation formats the amplitude and phase of the carrier are constrained to assume only certain values. DQPSK and .pi./4 DQPSK are examples of such modulation formats. An implication of such formats is that the controlling I and Q input values to the IQ modulator vary abruptly in discrete steps. If they were allowed to do so, however, the spectral content of the resulting carrier could easily contain excessive amounts of undesirable components that fall outside a permissible passband. Such undesirable spectral content is frequently referred to as "splatter". To reduce such splatter to acceptable levels it is common practice to include filters to smooth the transitions of the I and Q control inputs to the IQ modulator.
To transmit a stream of digital information (the "program" information) the incoming stream of data is collected into groups of n-many consecutive bits. Each group of n-many bits then represents one of 2.sup.n different possible data symbols that are the items of program data that are actually transmitted and received. An IQ encoder (or "mapper") in the transmitter trades the n-bit data symbols of program information for modulation state symbols that represent values of the I and Q control signals. A corresponding decoding mechanism ("reverse mapper") in the receiver trades the received modulation state symbol for its original n-bit sequence of program information. In many modulation formats the values of the I and Q control signals are each represented by one bit, so that a total of four different modulation state symbols are involved.
A communications channel having an IQ modulator at one end usually has an IQ demodulator at the other. It can be shown that the best signal to noise ratio for such a channel transmitting discrete symbols (i.e., a channel with digital modulation) is achieved when the channel, as a whole, is filtered according to a Nyquist filter whose half-power points are separated by half the symbol rate. Since it is desirable to incorporate identical filtering at each end of the channel, a root Nyquist filter is employed in both receiver and transmitter, to give the overall channel a combined Nyquist response.
A raised cosine filter meets these criteria, and has other desirable properties as well, if the roll-off value .alpha. is properly selected. It has been shown that for a symbol rate of 24.3 KHz a value of 0.35 for .alpha. is desirable for minimizing adjacent symbol interference while not unduly broadening the passband. (These parameters are, in fact, incorporated into the definition for the 30 KHz channel spacing NADC TDMA cellular telephone service.) To appreciate why this minimizes adjacent symbol interference it is useful to know that a Nyquist response implemented with a raised cosine filter involves the rather awkward notion of the filter beginning to produce an output before the symbol actually gets to the filter (so-called "negative time"). During this "negative time" the filter output periodically swings both above and below a quiescent level corresponding to no stimulus. Now, in an environment of consecutive modulation state symbols, whatever process for producing an output that the filter is following for the present symbol of interest, it is also still following for the symbol preceding that one, as well as for the symbol following the present symbol. All of these outputs add by superposition to form a composite value that is the present output of the filter. But, by arranging that each such swing (for symbols other than the symbol of present interest) has a zero crossing at the time that each present symbol is expected, these before and after swings in filter output always temporarily add to zero at those times when the output for the present symbol is expected. This summing to zero allows the filter's output to periodically represent only the present symbol, and then only the next present symbol, on so on. Thus, the output for the present symbol of interest is always produced at a time when residual outputs for adjacent symbols are zero.
A practical realization of such a filter is obtainable by capturing the last, say, eleven I and Q control values in shift registers having parallel outputs. After eleven input cycles the center I and Q values in these shift registers correspond to the present (albeit it not the newest) symbol. The I and Q values for the preceding five symbols are also present, as are the succeeding five symbols. All eleven values for I are applied to an "I filter", and all eleven values for Q are applied to a "Q filter". using all applied values, each filter acts on the center value, and its output is five symbols late, as it were. But this avoids the notion of "negative time". As new values are available they are shifted in and the oldest value is shifted out and discarded. Different systems may use different numbers of preceding and succeeding symbols, and those numbers need not be equal.
For the filter to do what is required, something therein must control the "trajectories" of the output I and Q control signals as they change from one value to the next in response to a changed input value. This is done by establishing what are called subintervals between the regularly scheduled changes in the values for I and Q. For example, the number of subintervals might be 16 (2.sup.4). The filter is now also supplied, as an input, with the four bits that define the current subinterval. The subinterval increments regularly according to a clock signal that runs an appropriate amount faster than the symbol rate. Thus the output of each filter can be a selected trajectory for the I and Q control signals that is, in part, a desired function of time that minimizes spurious frequency content in the modulated carrier signal.
An additional splatter control technique resides in the difference between simple DQPSK and .pi./4 DQPSK. For DQPSK each transmitted symbol corresponds to the change in phase between the (new) present symbol and the symbol that preceded it. Generally, a transmitted symbol represents two bits of phase information corresponding to phase changes of 0.degree., +90.degree., -90.degree. and 180.degree.. The problem is that this can require the extreme phase change of 180.degree. in the carrier to represent adjacent symbols, which in turn causes an undesirable amount of splatter.
In contrast, .pi./4 DQPSK never requires more than .+-.135.degree. of phase shift. This is accomplished by introducing an additional 45.degree. of phase shift between adjacent symbols. This constant underlying phase shift is termed "precession". Since the unit of precession is half of the 90.degree. used as the fundamental unit in representing modulation symbols, it results in a second set of four symbols interleaved between the original set. However, the trap of treating this as doubling of the number of symbols can be avoided, even though the constellation diagrams now have eight points instead of four. Since the precession causes an alternation between the two sets of four phase values, any current value in one of the sets has as a legitimate successor only the four values of the other set. Thus, the trick is to understand that although there are zero to seven (2.sup.3) instances of the precession's 45.degree., the demodulator in the receiver can map the eight points of the constellation diagram back into the original four symbols. However, the filters are presented with what now appears to be eight symbols, instead of four.
The filter for the .pi./4 DQPSK system described in the '613 patent to Birgenheier and Hoover represents this situation by using one bit each for I and Q, and three additional input bits to indicate the number of 45.degree. increments (modulo 8, or, relative to a reference location on the unit circle of the constellation diagram). The three bits indicating the number of 45.degree. phase shifts are necessary in their system because the mapper employed is the same as would be used for a DQPSK system (which has no precession), implying that the effective phase rotation caused by the precession in .pi./4 DQPSK must be accounted for in the filter.
As will be explained in the detailed description below, the approach used by the '613 patent causes the ROM based filters for .pi./4 DQPSK to use four times the number of addressable locations than are actually needed. It would be desirable if that additional memory could be eliminated to save size and cost, or if it could be used to provide extra functionality, instead.